Maths questions
Don't forget to take a ruler and calculator into the exam.
Maths questions often start with the command word calculate. You need to use numbers given in the question to work out the answer.
When an answer to a maths question is marked:
- full marks are given for the right answer
- marks may be given for working, including substitution and rearrangement
- errors carried forward are worked through to give credit for later working
Learn maths skills with Dr Alex Lathbridge
Listen to the full series on BBC Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting units.
Make sure you give answers to a suitable number of significant figures.
Maths questions might ask you to plot or complete a graph or table. When you draw a graph, make sure you:
- plot each point accurately
- draw a best fit straight line or curve, where appropriate
You may be given a grid with axes labelled and scales already given. Sometimes you may be given an empty grid for you to supply your own axes. When you do this:
- put the independent variable on the x-axis and the dependent variable on the y-axis
- choose even scales and make sure that the points cover at least half the given grid
- label the axes with their quantity and unit, eg time (s)
These questions have been written by Bitesize consultants as suggestions to the types of questions that may appear in an exam paper.
Sample question 1 - Foundation
Question
A student wants to find out the volume of hydrochloric acid that reacts with 25.0 cm3 of sodium hydroxide solution.
He carries out a titration. Table 1 shows his results.
| Titration 1 | Titration 2 | Titration 3 | Titration 4 | |
| Final burette reading | 37.60 cm3 | 36.20 cm3 | 39.15 cm3 | 38.40 cm3 |
| Initial burette reading | 1.80 cm3 | 0.00 cm3 | 3.95 cm3 | 2.10 cm3 |
| Volume of acid used | 35.80 cm3 | 36.20 cm3 | 35.20 cm3 | 36.30 cm3 |
| Final burette reading | |
|---|---|
| Titration 1 | 37.60 cm3 |
| Titration 2 | 36.20 cm3 |
| Titration 3 | 39.15 cm3 |
| Titration 4 | 38.40 cm3 |
| Initial burette reading | |
|---|---|
| Titration 1 | 1.80 cm3 |
| Titration 2 | 0.00 cm3 |
| Titration 3 | 3.95 cm3 |
| Titration 4 | 2.10 cm3 |
| Volume of acid used | |
|---|---|
| Titration 1 | 35.80 cm3 |
| Titration 2 | 36.20 cm3 |
| Titration 3 | 35.20 cm3 |
| Titration 4 | 36.30 cm3 |
a Which two results are within 0.10 cm3 of each other?
[1 mark]
Titration _____ and titration ______.
b Use your answer to part a to calculate the mean volume of acid required.
[2 marks]
a Titration 2 and titration 4. [1]
b mean volume = \(\frac{36.20 + 36.30}{2}\) [1]
= 36.25 cm3 [1]
Sample question 2 - Foundation
Question
A student electrolysed copper sulfate solution for five minutes.
Table 1 shows his results.
Table 1
| Anode | Cathode | |
| Mass of electrode before electrolysis | 1.16 g | 1.28 g |
| Mass of electrode after electrolysis | 0.85 g | 1.57 g |
| Mass of electrode before electrolysis | |
|---|---|
| Anode | 1.16 g |
| Cathode | 1.28 g |
| Mass of electrode after electrolysis | |
|---|---|
| Anode | 0.85 g |
| Cathode | 1.57 g |
Calculate the mass of copper deposited on the cathode.
[2 marks]
Mass deposited = 1.57 - 1.28 [1]
= 0.29 g [1]
Sample question 3 - Higher
Question
25.0 cm3 of 0.1 mol/dm3 sodium hydroxide solution reacts with 26.20 cm3 of sulfuric acid solution.
Calculate the concentration of the sulfuric acid, in mol/dm3.
[4 marks]
Volume of sodium hydroxide in dm3 = 25.00 / 1000 = 0.025 dm3
Amount of sodium hydroxide in mol = concentration in mol/dm3 × volume in dm3
= 0.1 mol/dm3 × 0.025 dm3
= 0.0025 mol [1]
The equation for the reaction is:
2NaOH(aq) + H2SO4(aq) → Na2SO4(aq) + H2O(l)
This shows that 2 mol of sodium hydroxide reacts with 1 mol of sulfuric acid. [1]
So the amount of sulfuric acid in 26.20 cm3 of solution = 0.5 × 0.0025 mol
The concentration of sulfuric acid = \(\frac{amount~in~mol}{volume~in~dm^3}\)
Volume in dm3 = 26.20 / 1000 = 0.0262 dm3
Concentration = \(\frac{0.00125~mol}{0.0262~mol}\)
= 0.0477 mol/dm3
Sample question 4 - Higher
Question
A student adds water to a sample of dilute hydrochloric acid.
The concentration of hydrogen ions decreases by a factor of 100.
Predict the effect on the pH.
[2 marks]
The pH increases. [1]
It increases by 2. [1]
